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To make the dressing, whisk the eggs in a medium bowl until fluffy. Gradually whisk in the vinegar a little at a time. Add the sugar, mustard, salt, and pepper; whisk until uniformly combined. Transfer the mixture to a 2-quart saucepan and place it over medium-low heat. Heat slowly, stirring constantly, until the mixture reaches a gentle boil. Continue cooking and stirring until the mixture thickens, about 1 minute. Cool, then stir in the sour cream.
Add dressing to slaw and mix well. Refrigerate the slaw for 1 to 2 hours. Serve slightly chilled.